Q12 of 45 Page 164

Let and be two lines intersecting at a point O. Let be a ray bisecting ∠BOD. Prove that the extension of to the left of O bisects ∠AOC.

11.JPG


OX is extended to OY


OX is bisector of ∠BOD


∴ ∠DOX = ∠BOX


From figure,


∠DOX =∠COY


And ∠BOX = ∠AOY


∴ ∠COY = ∠AOY


∴OY intersect ∠AOC


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Let be a line segment and let C be the midpoint of . Extend to D such that B lies between A and D. Prove that AD + BD = 2CD.

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Let be a ray and let and be two rays on the same side of , with between and . Let be the bisector of ∠AOB. Prove that

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